Theorems · Theorem · group theory
Subgroup.finiteIndex_of_finite_quotient
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G} [Finite (G ⧸ H)], H.FiniteIndex- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Finitestatement and proof · cited by 3,029
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Subgroup.FiniteIndexstatement · cited by 113
- Subgroup.index_ne_zero_of_finiteproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- Subgroup.IsComplement.finite_left_iffproof · cited by 3
- Subgroup.finiteIndex_iff_finite_quotientproof · cited by 2
- Subgroup.finiteIndex_of_leftCoset_cover_constproof · cited by 2
- IsPGroup.card_orbitproof · cited by 1
- Subgroup.IsComplement.finite_right_iffproof · cited by 1
- IsTopologicalGroup.exist_openNormalSubgroup_sub_clopen_nhds_of_oneproof · cited by 1